Separation and Renaming in Nominal Sets

3 Jun 2019Joshua Moerman and Jurriaan RotarXiv

Abstract

Nominal sets provide a foundation for reasoning about names. They are used
primarily in syntax with binders, but also, e.g., to model automata over
infinite alphabets. In this paper, nominal sets are related to nominal
renaming sets, which involve arbitrary substitutions rather than
permutations, through a categorical adjunction. In particular, the left
adjoint relates the separated product of nominal sets to the Cartesian product
of nominal renaming sets. Based on these results, we define the new notion of
separated nominal automata. These automata can be exponentially smaller than
classical nominal automata, if the semantics is closed under substitutions.